About two years ago, we went on the Discovery Creuise out of Ft. Lauderdale to Grand Bahama Island in Freeport. I have talked to other people that has cruised on Carnival and Royal Carribean said that they had to go through a drill with the life jackets on the beginning of the cruise. Why didn't the Discovery Cruise line do that?

maybe it's because Discovery sails on what is called a "short international voyage". This also applies to most cruise ferries in European waters, hence no lifeboat drills are being made but safety videos and/or presentations are shown.